Problem: Compute $\arctan \frac{2}{5} + \arctan \frac{5}{2}.$  Express your answer in radians.
Answer: Consider a right triangle with legs 2 and 5.

[asy]
unitsize(1 cm);

draw((0,0)--(5,0)--(5,2)--cycle);
draw((4.8,0)--(4.8,0.2)--(5,0.2));

label("$5$", (5/2,0), S);
label("$2$", (5,1), E);
[/asy]

One angle of the triangle is $\frac{\pi}{2},$ and the other two angles are $\arctan \frac{2}{5}$ and $\arctan \frac{5}{2}.$  Therefore,
\[\arctan \frac{2}{5} + \arctan \frac{5}{2} = \boxed{\frac{\pi}{2}}.\]